range versus standard deviation?

Question

my daughter is having difficulty with data sets
she needs to create two sets of data, x and y, where x has a larger std deviation than y, and y has a larger range. she can't seem to create the sets up that way. Please explain how to get the 'range'.

she needs to create two sets of data, x and y, where x has a larger std deviation than y, and y has a larger range. she can't seem to create the sets up that way. Please explain how to get the 'range'

I forgot to mention she can only have 6 numbers per set, and this is middle school math. :-)

Answer 1

In statistics, the range of a set of data refers to the smallest interval which contains all the data points, or to the width of that interval. For instance, the data set (0, 12, -37, 14, -9, 14.1) has the range [-37, 14.1], or just referring to the width of that interval, it has a range of 51.1. Note that the range only takes into account the largest and smallest values, whereas the standard deviation takes into account the variation among all the values. Thus, adding values which are exactly equal to the mean will reduce standard deviation, but will have no effect on the range. This gives you an easy method of controlling both variables. For instance, you might use:

x={-1, 1} (range 2, σ=1)
y={-2, 0, 0, 0, 0, 0, 0, 0, 0, 2} (range 4, ∑(x-μ)² = 8, σ² = 4/5, σ=2/√5) (the standard deviation may be made arbitrarily small by adding more zeros).

Edit: well why didn't you say only six numbers per set? Anyway, the basic principle remains the same -- for the set with larger standard deviation, shove all the values to the outside, and for the set with the larger range, cluster all the other values at the mean. For instance, you might use:

x={0, 0, 0, 9, 9, 9} (range 9, μ=9/2, σ=9/2)
y={0, 10, 5, 5, 5, 5} (range 10, μ=5, ∑(x-μ)² = 50, σ²=25/3, σ=5/√3)

Note that 5/√3<9/2, as required.

Answer 2

"Nominal" ability "in call" or "by using call"; at any fee, it ability having to do with the call of a few thing. It would not unavoidably propose "small"; the experience of the "nominal value" occasion given the previous answerer is that that's a cost in call purely, and would not meaningfully impact all of us's funds. the choice may well be a "important" value, which has substance and might need an impact. a extra powerful occasion of "nominal" may well be some thing like: the team of advisors, nominally the king's council, replaced into unable to come again to a style.

Answer 3

range = high value - low value


try x = {0,0,0,0,0,1,1,1,1,1,
2,2,2,2,2,3,3,3,3,3}
and y={0,1,2,3,3,3,3,3,3,3
,3,3,3,3,3,3,3,3,4,5}